What is the tangent of f(x)=(2x-3)/(2x+5),\at x=-1 ?

The tangent of f(x)=(2x-3)/(2x+5),\at x=-1 is y= 16/9 x+1/9

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tangent of f(x)=(2x-3)/(2x+5),\at x=-1

tangent of

f (x) = \frac{2 x - 3}{2 x + 5}, at x = - 1

y = \frac{16}{9} x + \frac{1}{9}

Solution steps

Find the tangent point:

(- 1, - \frac{5}{3})

Find the slope of

f (x) = \frac{2 x - 3}{2 x + 5} : \frac{df ( x )}{d x} = \frac{16}{( 2 x + 5 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{16}{9}

Find the line with slope m=

\frac{16}{9}

and passing through

(- 1, - \frac{5}{3}) : y = \frac{16}{9} x + \frac{1}{9}

y = \frac{16}{9} x + \frac{1}{9}

x \to 0 lim (3 x^{2} - 4 x + 5)

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\frac{d}{d x} (4 x^{3} - sin (x))

\int_{- 1}^{2} (x^{4} - 2 x^{3} + 2) d x

What is the tangent of f(x)=(2x-3)/(2x+5),\at x=-1 ?
The tangent of f(x)=(2x-3)/(2x+5),\at x=-1 is y= 16/9 x+1/9